DESCRIBING FUNCTIONS WORKSHEET

Describing functions worksheet :

The worksheet given in this section would be much useful to the students who would like to practice problems on "Describing functions as linear or non linear".

Describing functions worksheet - Problems

1. A square tile has a side length of x inches. The equationa y = x² gives the area of the tile in square inches. Describe whether the function represented by the above equation is linear or non linear. If it is linear, determine whether it is proportional.

2. The temperature of a fish tank was 82 °F and decreased steadily 2 °F every hour. The equation y = -2x + 82 gives the temperature y after x hours. Describe whether the function represented by the above equation is linear or non linear. If it is linear, determine whether it is proportional.

Describing functions worksheet - Solution

Problem 1 :

A square tile has a side length of x inches. The equation aaa y = x² gives the area of the tile in square inches. Describe whether the function represented by the above equation is linear or non linear. If it is linear, determine whether it is proportional.

Solution :

Step 1 :

To describe whether function represented by the equation is linear or non linear, let us graph the given equation.

Choose several values for the input x. Plug these values for x in the equation to find the output y.

x

1

2

3

4

x²

1²

y

1

4

9

16

(x, y)

(1, 1)

(2, 4)

(3, 9)

(4, 16)

Step 2 :

Graph the ordered pairs. Then draw a line through the points to represent the solutions of the function.

Step 3 :

Describe the relationship between x and y.

The graph is not a line. So the relationship between the side length of the square and its area is non linear.

Only a linear relationship can be proportional. Since the relationship is non linear, it is not proportional.

Hence, the function represented by the equation y = x² is non linear.

Problem 2 :

The temperature of a fish tank was 82 °F and decreased steadily 2 °F every hour. The equation y = -2x + 82 gives the temperature y after x hours. Describe whether the function represented by the above equation is linear or non linear. If it is linear, determine whether it is proportional.

Solution :

Step 1 :

To describe whether function represented by the equation is linear or non linear, let us graph the given equation.

Choose several values for the input x. Plug these values for x in the equation to find the output y.

x

0

1

2

3

4

5

-2x + 82

-2(0) + 82

-2(1) + 82

-2(2) + 82

-2(3) + 82

-2(4) + 82

-2(5) + 82

y

82

80

78

76

74

72

(x, y)

(0, 82)

(1, 80)

(2, 78)

(3, 76)

(4, 74)

(5, 72)

Step 2 :

Graph the ordered pairs. Then draw a line through the points to represent the solutions of the function.

Step 3 :

Describe the relationship between x and y.

The graph is a line. So the relationship between the time and the temperature is linear.

But the line is not passing through the origin. So, it is not proportional.

Hence, the function represented by the equation y = -2x + 82 is linear, but it is not proportional.

Note :

The graphs of all linear relationships will be a line. If the line passes through the origin, the linear relationship is proportional.

If the line does not pass through the origin, the linear relationship is non proportional.

After having gone through the stuff given above, we hope that the students would have understood "Describing functions worksheet".

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